The correct spelling of the two words "itching fight" is straightforward. "Itching" is spelled with the phoneme /ɪtʃ/ and refers to the sensation of an annoying skin irritation. "Fight" is spelled with the phoneme /faɪt/ and denotes a physical or verbal conflict. The two words together form an idiomatic expression that means engaging in a contentious argument or heated debate. The pronunciation of the two words combined is /ˈɪtʃɪŋ faɪt/.
The term "itching fight" does not have a specific etymology; it appears to be a colloquial phrase with a literal meaning. In English, "itching" is often used metaphorically to describe strong desire or a restless feeling. Similarly, "fight" refers to a physical altercation or conflict. When combined, "itching fight" might suggest a strong desire or intense urge to engage in a fight. However, it is worth mentioning that this term is not commonly used and may be specific to certain regions or dialects.